Year-long plan for Geometry Enriched College Prep





Days
Vocabulary
Key Concepts
Textbook Problems
Resources
Notes/Comments
CH 1



P12:1-36

*We will skip 1.6,1.7 until later
1.1
2
point
line
plane
collinear
coplanar
space
postulate
-Name points, lines, planes
-Use correct notation
-Name intersections
-Identify collinear, coplanar
sets of points, lines
-Sketch and label points,
lines, planes
-Determine whether
statements are always,
sometimes, or never true
P8:13-21
P9:26-39,43-38
P11:57-61

P129:24-29 (need more)
P131:48-49
p13
*We will include postulates on
P125 in CH 2 at this time
1.2
1
segment
between
congruent seg.
construction
-Apply "M is between P and
Q iff PM+MQ=PQ."
-Distinguish equal, congruent
-Use correct notation and
geometric symbols
-Use algebra to solve seg.
problems
P19:14-19, 21-32
P17: construction
P20:34
*omit measuring with rulers
*omit p22-24
1.3
2
distance
midpoint
seg. bisector
right triangle
legs
hypotenuse
-Find distance on a number
line
-Find distance in the coor.
plane
-Find the midpoint of a seg.
on number line and in coor.
plane
-Simplify square roots
-Use algebra to solve seg.
problems
-Given one endpoint and the
midpoint of a seg.,find the
other endpoint
-Identify segment bisector,
congruent segments
-Locate and identify legs
and hypotenuse of rt. tri.
-Apply the Pythagorean
Theorem
P16:1-23
P20:1-6 (more needed)
P31:13-30
P32:33-56
P33:63
P34:68,70,72
P30:construction
P34:71
*cover basic Pyth.
Theorem here
*make connection bt
Pythagorean theorem
and distance formulas
1.4
1
ray
opposite rays
angle
sides of angle
interior of angle
exterior of angle
vertex
degree
right angle
obtuse angle
acute angle
angle bisector
cong. angles
-Name rays, angles, op. rays
-Measure and classify angles
-Identify angle bisector,
congruent angles
-Use algebra to solve angle
problems
P41:12-29
P42:30-35,37-42
P43:45-46,50-53
P39: construction
P40: construction

1.5
2
adjacent angles
linear pair
vertical angles
complementary
supplementary
perpendicular
-Identify and solve problems
involving special angle pairs
-Prove "Vertical angles are
congruent."
-Solve word problems using
angles pairs
-Solve problems with perp.
lines
-Make correct
assumptions (see P49)
P51:8-17,19-26
P52:27-32,34-41
P53:49-52
P55: construction
DG: pgs 49-50

CH 2





*consider alternative
assessments for CH 2
*We will do open notes
assessment
over proofs all year
2.1
.5
inductive reas.
conjecture
counterexample
-Make a conjecture based
on a pattern
-Find a counterexample to a
conjecture
-Identify and use inductive
reasoning
P93:14-27 some of
P94:31-34,40-43
P95:53
DG: pg 96-113


2.2
.25
statement
truth value
negation
Venn diagrams
-Interpret a Venn diagram
-Negate a statement
P102:31,33
P103:48

*omit conjunction,
disjunction
2.3
1.25
conditional
statement
if-then
hypothesis
conclusion
converse
inverse
contrapositive
logically equiv.
biconditional
-Write a conditional in if-then
form
-Write the related
conditionals
-Identify which cond. are
logically equivalent
P110:22-31,35-38
P111:39-52
P112:59-61,62,65-67
P114:1-3

*include all related
conditionals
2.4
.5
deductive reasoning
prove
-Distinguish inductive/
deductive reasoning
-Apply law of detachment
and syllogism (need not
know the names)
P120:10-21
P121:29-34
(proofs should be
guided/done together)
DG: pg 114


2.5
.5
proof
theorem
-Explain the proof process
P129:30-31


2.6
1
algebraic proof
two-column proof
-Identify by name properties
of real numbers
-Identify and apply reflexive,
symmetric, and trans. prop.
of equality
-Fill in the blanks of a two-
column proof
-Write a two-column proof
with assistance
P137:9-12
P138:13-19
P139:23-26


2.7
1
Segment Addition
-Apply reflexive, symmetric,
transitive to segment cong.
-Write a two-column proof
P145:4
P146:6-7,9-12
P147:19

*help students create and
continually update a list
of properties, definitions,
theorems, etc. that can be
used in proofs. This is their
"Open Notes."
2.8
1
Angle Addition
Cong. Sup. Theor.
Cong. Comp.
Theor.
Vertical Angles
Theor.
-Apply reflexive, symmetric,
transitive to angle cong.
-Prove key
theorems P151 and P153
P155:14-19,22-26
P156:33-34
DG: pg 122


CH 3





*group 3.1,3.2,
3.5 on one quiz
*group 3.3,3.4,3.6 on other
3.1
1
parallel lines
skew lines
parallel planes
transversal
interior angles
exterior angles
cons. int. angles
alt. int. angles
alt. ext. angles
corr. angles
-Identify and name the
relationships between
pairs of angles formed
by a transversal
-Identify and name
relationships between
lines and planes
P174:13-36
P175:38-43,46-50
DG: pg 128


3.2
2
Corr. <s post.
Alt. int. <s ther.
Cons. int. <s ther.
Alt. ext. <s ther.
-Discover, prove and apply
key post. & theorems (P179)
-Use algebra to solve
angle problems
P181:11-19
P182:24-30,35
P183:37-39,42,44,46
P177 GSP

3.3
1
slope
rate of change
-Find slope of a line from
a graph
-Know and use slope form.
-Recognize and name 4
different types of slope
(+,-,0, und.)
-Use slope to determine
whether lines are par. or
perp.
P191:12-25,28-33
P192:34-35
P185 lab

3.4
2
slope-intercept form
point-slope form
-Write the equation of a line
in slope-intercept and/or
point-slope form
-Write equations of a line
parallel or perp. to a line
through a point
-Graph lines and write
equation from a graph
-From equations, tell if
lines are par., perp., or
neither
-Write the equation of a
perp. bisector of segment
P200:13-30
P201:31-40,43-49
P202:50-53,56,57,59
P204:1-6

*be sure
to use point-slope when
appropriate
*Cover P204
3.5
2
converses of 3.2
-Discover, prove and apply
key post. and theorems
P205 and P206
-Given select angle
measures, determine
which lines are parallel
-Prove lines parallel
-Solve related alg. probs.
P209:8-21,23
P210:25-28,30-31,33-35
P211:38,40,41-43
P205: construction

3.6
.5
equidistant
-Sketch segment that is
distance from a
point to a line
-Solve a system of linear eq.
by graphing, subst., elim.
P218:9-12
P18:1-15
P214: construction
P220:36-37

CH 4
7
3 r
3 q/t




*Cover 4.7 later
*skip 4.8
*Group 4.1-4.5 on 1st quiz
*Group 4.6, 5.3,5.5,5.6 on 2nd
4.1
.5
acute triangle
equiangular triangle
equilateral triangle
obtuse triangle
right triangle
isosceles triangle
scalene triangle
-Classify triangles by side
and/or angles
-Solve alg. problems
involving triangle sides
-Sketch each triangle type
and the possible
combinations
P239:15-26,30-37
P240:40-46,49-52
P241:57-64
P240:53 construct.

4.2
1
exterior angle
remote int. angles
flow proof
-Discover, prove and apply
Triangle Angle-Sum theor.
and Ext. Angle Theorem
-Complete with guidance a
flow proof
-Solve algebra problems
involving triangle angles
P248:12-15
P249:17-22,24-29
P250:30-32,34-40
P251:44,47,49,50,51
P243 good to do

4.3
.5
cong. polygons
corr. parts
CPCTC
-List cong. corr. parts of 2
congruent triangles
-Prove two triangles cong.
using CPCTC
P257:9-16
P258:21-24
P259:40-41

*skip algebra probs in this
section
4.4
.5
1.5 p
included angle
SSS
SAS
-Explore and apply SSS
and SAS
-Prove triangles congruent
using SSS and SAS
P267:5,6,8-13
P268:14-19,21-22
P269:24-26,30,
P264 construction
P265 construction
P269:32 const.
P271 const. proofs
*we have in the past
taught the ways to prove
on one day and done
proofs the next day
*not many non-proof
problems
*harder proofs such as
overlapping are mixed in
*skip algebra probs here
4.5
ext
.5
1.5 p
included side
ASA
AAS
HL
-Discover and apply ASA
and AAS
-Prove AAS
-Prove triangle congruent
using ASA and AAS
-Explore right triangle cong.
-Prove and apply HL
P277:6-7,9-11
P278:12
P279:17-20,24-25
P282:7-9,13-15
P273 construction
P281 lab
*helpful table on P276
*only HL is different,
teach only it
4.6
1
legs of isos. tri.
base of isos. tri.
vertex angle
base angles
Isosceles Triangle
Theorem
-Discover, prove and apply
isos. tri. theor. and converse
-Discover and apply
corollaries about equil. tri.
-Solve related algebra probs
P287:9-14
P288:15-24
P289:29-32,34,38-39
290:49-50
P289:27 const.
P292-293 Inspire

4.7
1
transformation
cong. trans.
preimage
image
reflection
translation
rotation
-Define and recognize the
congruence transformations
-Perform a congruence
transformation in a plane
P297:7-12
P298:17-20
P299:32-36

*Cover at beginning of CH 9
*Students should do
some transformations on
patty paper and in GSP
CH 5





*skip 5.4 indirect proof
*CH 5 is short; combine w
CH 4
*combine 5.3,5.5,5.6
with CH 4
*alternative assessment
of 5.1-5.2
5.1
2
perp. bisectors
concurrent lines
point of concurrency
angle bisector
circumcenter
incenter
-Sketch the perp. bisectors
of a triangle and find the
circumcenter
-Sketch the angle bisectors
of a triangle and find the
incenter
-Discover, prove and apply
the perp. bisector and angle
bisector theorems
-Discover the circumcenter
and angle bisector theorems
-Write the eq. of the perp.
bisector
P327:9-14
P328:21-26
P329:37,39,40
P330:50-51
P321 constructions
*sketching NOT true
constructing
*sketch practice in handouts
5.2
1
median
centroid
altitude
orthocenter
-Sketch the medians
of a triangle and find the
centroid
-Sketch the altitudes
of a triangle and find the
orthocenter
-Describe the location
of the pts of concurrency in
acute, obtuse and right
triangles
-Discover the centroid theor.
-Write the eq. of the median
and altitude
P338:5-10
P339:27-31
P340:38,42
P332 constructions
*helpful table P337
*do NOT find pts of concurr. in
coor. plane
*write eq. of concurrent
lines; problems on handout
5.3
.5

-Explore and apply key
theorems (P343,344)
-Given sides, list angle
measures from least to
greatest
-Given 2 angles, list sides
from shortest to longest
P346:8-19
P347:22-37
P348:39-41,46-48

*need more like P348:41
*skip prop. of inequality
*No ineq. proofs assigned
to students
5.5
.5
Tri. Ineq. Theorem
-Discover and apply the
Tri. Ineq. Theorem
-Given 2 side lengths, fine
the range of the 3rd side
P363:6-17
P364:25-26
P365:38-41,44,45
P359 TI-84
*avoid proofs w ineq.
5.6
.5
Hinge Theorem
-Explore and apply Hinge
Theorem and converse
P372:10-15
P374:31-33,41

*cover this section
CH 6





Spring Semester begins
1.6
.5
polygon
vertex
concave
convex
n-gon
equilateral
equiangular
regular
-Classify polygons as
convex/concave, regular/not
-Define and identify a polygon
-Name a polygon by # of
sides up to 12
P61:11-16
P63:46-47


6.1
1.5
exterior angles
Polygon Int. < Sum
Polygon Ext. <
-Discover, derive and prove
for a specific polygon the
Interior Angles Sum Theor.
-Discover and prove for a
specific polygon the Ext.
Angles Sum Theorm
-Apply the Int. and Ext.
< Sum theorems
to regular and irregular poly.
-Given the measure of an
int. or ext. angle of a reg.
poly.find the number of sides
-Solve related algebra probs.
P394:12-19,21-24,26-29
P395:30-37,39-43,45,46
P396:50,51
P398 Excel

6.2
1
parallelogram
diagonal
opposite
consecutive
-Define and sketch a par.
-Discover, explore and prove
key theorems about par. on
P399 and P401
-Solve relate alg. probs.
-Analyze par. in the coor.
plane
-Apply properties of par.
to find missing sides/angles
P403:9-12
P404:15-20,23-24
P405:26-37
P406:39,42,43
P408 TI 84
*P404:21-22?
6.3
1

-Discover, explore and prove
key theorems about proving
a quad is a par. P409
-Determine whether a
quad must be a par.
-Prove a quad is a par.
-Determine whether a
quad in the coor. plane
is a par.
-Find missing vertices
of a par. in coor. plane
-Solve related alg. probs.
P414:9-16,18-20
P415:21-27,30,32-33,
35-36
P416:41,44
P415:34 const
*P411 helpful table
*skip coor. proofs
6.4
1
rectangle
-Define and sketch a rect.
-Discover and prove that
diagonals of a rect. are
congruent
-Discover and prove that a
par. with cong. diagonals is
a rectangle
-Solve related alg. probs.
-Prove a par. is a rect.
-Determine whether a quad
in coor. plane is a rect.
-Find the missing vertices of
a rect in coor. plane
-Apply properties of rect
to find missing sides/angles
P422:10-19
P423:20-31,33-36,39-40
P424:48-49
P423:37 const

6.5
1
rhombus
square
-Define and sketch a
rhombus and square
-Discover and prove key
theorems P426,428
-Apply prop. of rhombus
and square to solve for
missing sides/angles
-Solve related alg. probs.
-Find missing vertices in
coor. plane
-Determine if quad. in coor.
plane is a square or rhombus
-Prove a par. is a rhombus
or square
P431:7-16
P432:19-30,34-38
P433:47
P432:39-40 const
*P427: Venn diagram
6.6
2
trapezoid
kite
bases
legs of trapezoid
base angles
isosceles trapezoid
midsegment of trap
-Define and sketch a kite,
trapezoid, and isos trap
-Discover and prove key
theorems P435,437,439
-Apply prop. of kites, traps,
and isos. traps to find
missing sides/angles
-Solve related algebra probs
-Find missing vertices in
coor. plane
-Determine if quad in coor.
plane is kite or trap or isos.
-Prove a shape is a trap, kite
or isos. trap
P440:8-15
P441:16-21,24-32,34
P442:35-57
P443:59-61,67,68

*cover midsegment
*need more always,
sometime, never practice
CH 7





*no proofs for students in
this chapter
*skip most of 7.5
*skip 7.6, covered in CH 9
*skip 7.7 or do as project
7.1
.5
ratio
proportion
proportional
cross product
equivalent prop.
-Solve a proportion
-Apply a ratio
P461:21-28,31-33
P462:47,48


7.2
1
similar
similarity ratio
scale factor
similarity statement
-Define and recognize
similar polygons
-Determine if two polygons
are similar
-Write a similarity statement
-Use similarity to find
missing sides/angles/
perimeter
-Discover propotionality
of perimeter of sim shapes
P469:8-15
P470:18-28
P471:29-30,35,36,40-45
P472:53,54

*avoid student proofs with ratios
7.3
.5
AA Sim
SSS Sim
SAS Sim
-Explore AA Sim
-Explore and discuss proof
of SSS Sim and SAS sim
-Apply key post. and
theorems to prove triangles
similar
-Determine whether triangles
are similar or not
P479:9-11
P480:12-14,16,17

*skip reflex, trans, symm
*P478 helpful table
*careful about how
difficult algebra gets
7.4
1
midsegment of tri.
-Discover and prove key
theorems P484,485
-Discover corollaries about
parallel lines and prop.
-Apply key concepts to
set up and solve prop.
P489:10-13
P490:14-21
P491:33-38
P488 construction
P492:44-46

7.5
.5
Tri. Angle Bisector
theorem

P499:11-14
P500:20-23

*only cover theorem 7.11
on P498
*omit prop. of special
segments
CH 8





*NO student proofs
*omit 8-6,8-7
8.1
2
geometric mean
-Find the geometric mean of
two numbers
-Discover, prove and apply
theorem 8.1, P532
-Explore and apply key
theorems P533
P535:8-17
P536:18-23
P536:29-30

*watch difficulty of algebra
*review simplifying square
roots and rationalizing
8.2
1
Pythagorean triple
-Explore and apply Pyth.
Theorem (consider proving)
-Recognize a Pyth. triple
-Discover and apply converse
of Pyth theorem and ineq.
theorems, P544
-Classify a triangle as acute,
right, obtuse from side
lengths
P546:9-12,15-18
P547:21-33
P548:51
P540 hands on
*omit P550-551
8.3
2

-Discover and derive formulas
for 45-45-90 and 30-60-90
triangles
-Find the missing sides of
special right triangles
P556:8-17
P556:18-25,28-33
P557:37-38,41,43


8.4
1.5
trigonometry
trig ratio
sine
cosine
tangent
inverse sine, cos,
tan
-Memorize and apply trig
ratios
-Use trig to find missing
sides and angles in rt tri.
P567:16-21
P568:22-33,36-41
P569:42-45
P570:57-59
P561 TI-84
*omit P569:47-49
*omit P572
8.5
1.5
angle of elevation
angle of depression
-Apply trig to word problems
involving angles of elevation
and depression
P577:4-8
P578:all
P579:all

*need some problems
where student provides/draws
picture
CH 9





*cover 4.7 first
*skip 9.4,9.5,tesselations
*skip 9.6, cover with CH 7
*no proofs
*did not cover in 2010-2011
due to snow week
9.1
1
line of reflection
-Perform reflections
-Perform reflections in coor.
plan over axes and y=x
-Discover patterns in
coordinates as points
are reflected over axes or
y=x
P619:10-15
P620:18-29


9.2
1

-Perform translations
-Perform translations in
coor. plane
-Discover how to manipulate
coordinates


*can be taught without
vectors?
9.3
1
center of rotation
angle of rotation
-Perform rotation
-Perform rotations in coor.
plane
-Discover how to change
coordinates for 90, 180
and 270 degrees
P635:5-10
P636:14-19
P637:37
P631: hands on

CH 10





Students do informal or
paragraph proofs in this
chapter
10.1
.5
circle
center
radius
chord
diameter
congruent circles
concentric circles
circumference
pi
-Identify and name the parts
of a circle
-Find the circumference of
a circle
-Define and identify cong.
and concentric circles
-Relate radius, diameter,
and circumference
-Find circumference using
inscribed/circumscribed
shapes
P687:10-17
P688:18-21,28-33,36-39
P689:51


10.2
.75
central angle
arc
arc length
minor arc
major arc
semicircle
congruent arcs
adjacent arcs
-Identify, name and measure
arcs and central angles
-Find arc length
-Prove theorem 10.1, P693
-Apply Arc Addition Post.
-Solve related alg. probs.
P696:12-15
P697:16-23,26-41
P698:45-50,52
P699:56-58


10.3
.75

-Prove and apply key
theorems, P701-703
P705:7-14,16-19
P706:22-26
P707:29-32
P704:construction

10.4
1.5
inscribed angle
intercepted arc
inscribed polygon
-Prove and apply inscribed
angle theorem and other key
theorems, P710,711,712
P713:11-13
P714:14-31
P715:36-40

*students will need more
practice
10.5
.5
tangent
point of tangency
common tangent
circumscribed poly.
-Explore and apply theorem
10.10, P719 (proof is indirect)
-Prove and apply theorem
10.11, P720
-Sketch common tangents
-Find the perimeter of a
circumscribed polygon
P722:9-16
P723:17-22,24-29
P724:35,39
P720:construction

10.6
1
secant
-Prove and apply key
theorems concerning angles
formed by tangents, secants
P727-729
P732:8-16,18-23
P733:30-33
P734:37-39

*helpful table P731
10.7
1

-Explore and apply key
theorems relating lengths
of segments formed by
tangents, secants, P736,738
P740:6-13,16-21

*Students do not do these
proofs
10.8
1

-Derive and apply the
equations of a circle
-Given endpoints of a
diameter, write the eq.
P747:11-18,21-24,27,34
P743 NSpire
*Omit eq. from 3 pts,
CH 11


*derive formulas whenever
possible


*Cover 1.6 perimeter and area
first
1.6
.5
perimeter
area
-Find perimeter and area
of squares and rectangles
-Solve related word problems
-Given P or A and some
dimensions, find missing one
-Find P and A in coor. plane



11.1
1
base of par./tri.
height of par./tri.
-Find the perimeter and area
of parallelograms and
triangles
-Explore postulates on P763,
P765
-Given area and base or
height, find missing base
or height
-Use trig or special triangles
to find missing height
-Solve word problems
related to perimeter and area
-Find area of shape in
coor. plane
P767:10-15
P768:17-22,24-27,30-32
P769:33-34,39-40
P771 TI NSpire
*exact form won't work
when using trig
*need some problems where
Pyth. Theorem is used
11.2
1
height of trapezoid
bases of trapezoid
-Find perimeter and area of
trapezoids, rhombi, kites
-Given area and all but one
dimension, find missing
dimension
-Use trig or special rt. tri.
to find missing height
-Solve word problems
related to perimeter and area
-Find area of shape in
coor. plane
P777:8-13
P778:18-21,23-24,26-27
P779:35,36,38

*Skip Area of Rhombus/Kites
*Helpful table P776
*omit dimensional analysis
*do more like P779:35, given
one h in par. find the other
11.3
1
sector of a circle
segment of a circle
-Find the area of a circle
-Find the area of a sector
or segment of a circle
-Given area of a circle, find
r or d
P785:14-23
P786:27-29,32-37
P787:40-42,45,46


11.4
2
center of reg. poly.
radius of reg. poly.
apothem
central angle
composite figure
-Find the area of a regular
polygon using trig or
special right triangles
-Find the area of composite
figures
P795:8-9
P796:10-13,15-20
P797:22-24

*omit P800-801
11.5
1

-Discover relationship
between area of similar
shapes
-Find the area of similar
shapes utilizing the scale
factor
-Given areas of similar
shapes, find scale factor
and missing dimensions
-Solve related word problems
P805:6-13
P806:14-15


CH 12





*Cover 1.7 first
*omit 12.1
*omit 12.7
*derive formulas when
possible
1.7
1
polyhedron
face
edge
vertex
prism
base
pyramid
cylinder
cone
sphere
surface area
volume
-Identify, name, and
analyze 3-D solids
P71:6-17
P821 drawing solids by hand
*omit platonic solids
*omit formulas, to be covered
in next sections
12.2
1
2 c
lateral face
lateral area
composite solid
-Find lateral area and
surface area of prisms
and cylinders
-Given LA or SA and some
dimensions, find missing one
-Solve related word problems
-Find surface area of
composites
P834:9-22
P835:24-27
P836:35-37


12.3
1
regular pyramid
slant height
right cone
-Find lateral area and
surface area of reg.
pyramids and right cones
-Given LA or SA and some
dimensions, find missing one
-Solve related word problems
-Use slant height and
altitude to find dimensions
of regular base
-Find surface area of
composites
P843:7-12
P844:14-17,23-25
P845:33-34

*helpful table P842
*composites after
cones and pyramids
12.4
1
1 c

-Find volume of prisms
and cylinders
-Given volume and some
dimensions, find missing one
-Solve related word problems
-Find the volume of
composites
P850:10-15
P851:16-19,21
P852:28-30,32-34

*include obliques
*cover composites after
12.5
1

-Find volume of pyramids
and cones
-Given volume and some
dimensions, find missing one
-Solve related word problems
-Find the volume of
composites
P860:10-16
P861:17-22,26-28
P862:32-34

*helpful table P859
12.6
.5 SA
.5 V
great circle
hemisphere
-Find SA and V of spheres
and hemispheres
-Given SA or V, find r
-Given SA or V, find the other
-Solve related word probs
-Find V and SA of
composites with spheres
and hemispheres
P868:10-25
P869:29-30

*cover SA with SA sections
*cover V with V sections
12.8
2
similar solids
-Discover relationship
between SA and V of similar
solids
-Find SA or V of similar
solids using scale factor
-Given SA or V of similar
solids, find scale factor
and missing dimensions
-Solve related word problems
P883:6-13
P884:20-21